Coupled Oscillator Model Research Articles

Sonority sequencing and its relationship to articulatory timing in Georgian

This work asks how the syllable as a unit is delimited in space and time. To do this we bring together two theoretical approaches to the syllable: a sonority-based approach which emphasizes spatial organization, and the coupled oscillator model (Nam, Goldstein & Saltzman 2009) which emphasizes temporal organization. Many languages present challenges to these theories, and here we focus on Georgian, which is problematic for both approaches, as Georgian permits onset clusters of up to seven consonants and of any sonority shape. Specifically, this study examines the relationship between gestural overlap and sonority shape in Georgian via electromagnetic articulography. Drawing on data from three speakers, we examine gestural overlap in two-consonant onsets that vary in sonority shape and order of place of articulation. Using two measures of gestural overlap, we find (i) long lag between consonant gestures, which we suggest is language-specific and (ii) that lag is largest in sonority rises and smallest in sonority falls. These results suggest that neither phonemic recoverability nor a hierarchical effect of increasingly open constrictions is the primary motivator behind inter-consonantal timing. Instead, the high degree of overlap in sonority falls ensures their tautosyllabic parse, which would otherwise be threatened by intrusive vocoids. Thus, we argue that recoverability of the syllable as a unit is the major motivating factor behind the timing patterns observed, and that syllables emerge not solely from either spatial or temporal properties, but from the interplay of the two.

Droplet superpropulsion in an energetically constrained insect

Food consumption and waste elimination are vital functions for living systems. Although how feeding impacts animal form and function has been studied for more than a century since Darwin, how its obligate partner, excretion, controls and constrains animal behavior, size, and energetics remains largely unexplored. Here we study millimeter-scale sharpshooter insects (Cicadellidae) that feed exclusively on a plant’s xylem sap, a nutrient-deficit source (95% water). To eliminate their high-volume excreta, these insects exploit droplet superpropulsion, a phenomenon in which an elastic projectile can achieve higher velocity than the underlying actuator through temporal tuning. We combine coupled-oscillator models, computational fluid dynamics, and biophysical experiments to show that these insects temporally tune the frequency of their anal stylus to the Rayleigh frequency of their surface tension-dominated elastic drops as a single-shot resonance mechanism. Our model predicts that for these tiny insects, the superpropulsion of droplets is energetically cheaper than forming jets, enabling them to survive on an extreme energy-constrained xylem-sap diet. The principles and limits of superpropulsion outlined here can inform designs of energy-efficient self-cleaning structures and soft engines to generate ballistic motions.

Coupled-oscillator model for hybridized optical phonon modes in contacting nanosize particles and quantum dot molecules

Modification of optical phonon spectra in contacting nonpolar nanoparticles compared to single particles is studied. Optical phonons in dielectric and semiconducting particles obey the Euclidean metric Klein-Fock-Gordon equation with Dirichlet boundary conditions. This equation is supposed to be solved numerically for manifolds of cojoined spheres. It is proposed to replace this problem with the simpler-to-solve coupled-oscillator model (COM), where an oscillator is attributed to each phonon mode of a particle and the particle overlap leads to the appearance of additional couplings for these oscillators with the magnitude proportional to the overlap volume. For not too big overlaps, this model describes solutions of the original eigenvalue problem with a quantitative level of accuracy. In particular, it works beyond isotropic $s$ modes in dimers, which has been demonstrated for $p$ modes in dimers and for tetramers. It is proposed to apply the COM for the description of recently manufactured dimer nanoparticles and quantum dots. The obtained results are in agreement with the dynamical matrix method for optical phonons in nanodiamonds. The dynamical matrix method is also used to demonstrate that the van der Waals contacts between faceted particles lead to very small modifications of the optical phonon spectra, which therefore could be neglected when discussing the propagation of vibrational excitations via a nanopowder. The possibility to distinguish between dimerized and size-distributed single particles from their Raman spectra is also considered. The proposed COM paves a way towards the description of propagation of vibrational modes in the ensembles of particles in contact including tight agglomerates, nanocrystal solids, and porous media.

Coherent coupling between surface plasmons and localized surface plasmons in black phosphorus metamaterials

We propose a hybrid structure supporting electromagnetic coupling between black phosphorus surface plasmons (BPSP) mode and localized surface plasmons (BPLSP) mode theoretically. By dynamically controlling the carrier concentration of the black phosphorus strip, we show the coherent BPLSP-BPSP mode coupling. The coherent coupling can be described by using the coupled oscillator model, which shows a distinct Rabi splitting phenomena with frequency of 8.7 THz. The coherent coupling between BPLSP mode and BPSP mode also leads to the formation of multiple hybrid modes. In addition, we also explore the influence of structural parameters on coherent coupling. Our work may provide a reference for the interaction between different mode coupling.

Cavity-assisted boosting of self-hybridization between excitons and photonic bound states in the continuum in multilayers of transition metal dichalcogenides

Strong coupling between excitons in transition metal dichalcogenides (TMDs) and quasibound states in the continuum (QBIC) has attracted much attention in recent years. However, the coupling strength is often limited due to the spatial mismatch at the location of the TMDs and the maximum field strength of the QBIC mode. Here, we report a cavity-assisted boosting of self-hybridization between excitons (X) and the QBIC mode at room temperature by embedding a two-dimensional (2D) metasurface composed of bulk ${\mathrm{WS}}_{2}$ into a microcavity. We demonstrate that the self-hybridized BIC-X coupling strength in this 2D metasurface can be dramatically enhanced with the assistance of a Fabry-P\'erot cavity. Full wave simulations demonstrate a giant Rabi splitting up to 240 meV, which is twice as high as the QBIC-X self-hybridization in the 2D metasurface system. A coupled oscillator model containing a $3\ifmmode\times\else\texttimes\fi{}3$ Hamiltonian matrix combined with a near-field analysis reveals the underlying mechanism of the greatly enlarged coupling strength: The cavity provides a strong out-of-plane field confinement and the QBIC mode concentrates in an in-plane electric field, which greatly facilitates the spatial overlap of excitons with the localized field. Importantly, we also demonstrate that the coupling strength of the hybrid system can be readily tuned by controlling the excitonic oscillator strength of the bulk TMD material. This provides a powerful approach for manipulating the self-hybridization process. We believe that the cavity-based configuration proposed in this paper can serve as a universal recipe for achieving strong light-matter interactions, thus paving the way for the design of tunable exciton-polariton photonic devices with high performance.

Parameter identification of two coupled oscillator model for pure intrinsic thermoacoustic instability

Thermo-acoustic instabilities are a well-known problem in combustions systems. In general, the type of these modes can be divided in two categories: (i) modes with an acoustic origin and (ii) modes with an intrinsic thermo-acoustic (ITA) origin. It is an challenging task to observe the ITA modes experimentally. Therefore, a setup with a burner in an acoustic embedding with close to anechoic up- and downstream terminations is required. In previous research we introduced such a setup and conducted an experimental bifurcation analysis on the dominant pure ITA mode. In this bifurcation analysis, we observed that for increasing upstream velocity the flames loose stability through a supercritical Hopf bifurcation and subsequently exhibit limit cycle, quasi-periodic and period-2 limit cycle oscillations. The quasi-periodic oscillations were characterized by low frequency amplitude and frequency modulation. In this research we present a phenomenological model consisting of two coupled oscillators that is able to reproduce all the different experimentally observed regimes. This model consists of a nonlinear Van der Pol oscillator and a linear mass-spring-damper oscillator, which are nonlinearly coupled to each other. Furthermore, we executed a parameter identification of the model and concluded that the model is able to describe the experimental data quantitatively well.

Analytical design and model analysis of dynamically tunable terahertz metal-graphene hybrid metamaterial

A dynamically tunable terahertz metamaterial structure, comprising a split ring resonator made of lossy metal and a graphene formed square ring resonator, is designed and proposed. Subsequently, the influence of geometrical parameters of the proposed metamaterial structure and electromagnetic properties of graphene on the tunable terahertz spectral characteristics are investigated in detail. Meanwhile, the use of the equivalent model can provide numerical alternative methods and theoretical support for the design, optimization, simulation, and verification of metamaterial devices. The performances of the unit cell and the metamaterial are studied by a coupled oscillator model and a semi-analytical transmission line model; the analytic results agree excellently with our numerical results using full-wave simulations. The dynamical adjustment capacity of terahertz transmission spectra depends on the tunable terahertz metal-graphene hybrid metamaterial, which allows for designing an efficient device for a wide range of specific tasks including applications in sensing and switching. Furthermore, a comprehensive analytical approach based on these models constructs a theoretical basis for the design of metamaterial structures in a wider range and supports the mutual verification of the fitting results.

From weak to strong coupling with enhanced dualband magnetoplasmonic Kerr sensing in the dimer-grating metamaterial

We investigate the evolution of plasmonic spectral features from weak to strong coupling regime, with a large Rabi splitting of 210 meV, in the designed dimer-grating metamaterial. The two-driven coupled oscillator model has been proposed to quantitatively analyze the evolution, where the two oscillators are directly excited by the external driving light wave, demonstrating that the evolution is caused by not only aligning the resonance wavelength of related SP modes, but also low-loss. The proposed metamaterial is of high magnetoplasmonic refractive index sensitivity of 280.05 nm RIU−1 and figure of merit of 3*104 RIU−1, suggesting promising applications in biochemical sensing.

Polarization-insensitive electromagnetically induced transparency-like and dual-band absorption based on graphene and vanadium dioxide metamaterials

In this work, a dynamically tunable and polarization-insensitive electromagnetically induced transparency-like (EIT-like) and dual-band absorption based on graphene and vanadium dioxide metamaterial is proposed. The unit cell of the metamaterial consists of two monolayer graphene square rings of different sizes. The transparent window results from the near-field coupling can be observed in the x and y polarization directions, respectively. The EIT-like effect can be tuned by changing the Fermi energy of graphene. The three-level Λ-type system and the distribution of the electric field on |Ez| are employed to explain the physical mechanism of the EIT-like effect clearly. The theoretical fitting results based on the coupled oscillator model are in good agreement with the numerical simulation results. In addition, by introducing vanadium dioxide (VO2) and utilizing the phase change property of VO2, the designed metamaterial can realize the transition from an analog of electromagnetically induced transparency to a dual-band absorber which has two absorption bands in the frequency range of 0.2–3 THz and the absorption rate reaches 63.2% at 0.96 THz and 99.6% at 1.89 THz. Furthermore, we investigate the performance of metamaterials to probe the refractive index of the surrounding medium and our prototype exhibits a highest sensitivity value of about 0.4845 THz/RIU. This proposed design provides a viable approach for developing slow-light devices, sensors, absorption, and multifunctional devices.

Multiple plasmon-induced transparency based on black phosphorus and graphene for high-sensitivity refractive index sensing.

A hybrid bilayer black phosphorus (BP) and graphene structure with high sensitivity is proposed for obtaining plasmon-induced transparency (PIT). By means of surface plasmon resonance in the rectangular-ring BP structure and ribbon graphene structure, a PIT effect with high refractive index sensitivity is achieved, and the surface plasmon hybridization between graphene and anisotropic BP is analyzed theoretically. Meanwhile, the PIT effect is quantitatively described using the coupled oscillator model and the strong coherent coupling phenomena are analyzed by adjusting the coupling distance between BP and graphene, the Fermi level of graphene, and the crystal orientation of BP, respectively. The simulation results show that the refractive index sensitivity S = 7.343 THz/RIU has been achieved. More importantly, this is the first report of tunable PIT effects that can produce up to quintuple PIT windows by using the BP and graphene hybrid structure. The high refractive index sensitivity of the quintuple PIT system for each peak is 3.467 THz/RIU, 3.467 THz/RIU, 3.600 THz/RIU, 4.267 THz/RIU, 4.733 THz/RIU and 6.133 THz/RIU, respectively, which can be used for multiple refractive index sensing function.

Self-assembled monolayer silver nanoparticles: Fano resonance and SERS application

Plasmonic response of noble metal nanoparticle are of fundamental interest in nanophotonic applications, such as photocatalysis, information storage, sensing, optical switches, and nonlinear optics. We comprehensively investigate the Fano resonance and SERS (surface–enhanced Raman scattering) application of self–assembled monolayer silver nanoparticles using commercial FDTD (finite difference time domain) solver, cartesian multipole decompositions method, two coupled oscillators model and experiments. We found that the higher–energy antibonding mode is not only from the antibonding dipole–dipole mode (ADD), but also from the antibonding quadrupole–quadrupole mode (AQQ) and the hybridized magnetic mode when the particle size is relatively large in homodimer, as for the heterodimer, the case will change even more. The effects of dimer gap and size are discussed in details. A two coupled oscillators model is used to illustrate the mechanism of the Fano resonance, and the energy storage as a function of radiation loss and intrinsic loss in the plasmonic system is qualitatively evaluated, which is directly related to the near–field enhancement. Finally, SERS (surface–enhanced Raman scattering) experiments are carried out to meet the numerical results, and the SERS performance is also investigated and given.

Synergetic synchronized oscillation by distributed neural integrators to induce dynamic equilibrium in energy dissipation systems

The synchronization phenomenon is common to many natural mechanical systems. Joint friction and damping in humans and animals are associated with energy dissipation. A coupled oscillator model is conventionally used to manage multiple joint torque generations to form a limit cycle in an energy dissipation system. The coupling term design and the frequency and phase settings become issues when selecting the oscillator model. The relative coupling relationship between oscillators needs to be predefined for unknown dynamics systems, which is quite challenging problem. We present a simple distributed neural integrators method to induce the limit cycle in unknown energy dissipation systems without using a coupled oscillator. The results demonstrate that synergetic synchronized oscillation could be produced that adapts to different physical environments. Finding the balanced energy injection by neural inputs to form dynamic equilibrium is not a trivial problem, when the dynamics information is not priorly known. The proposed method realized self-organized pattern generation to induce the dynamic equilibrium for different mechanical systems. The oscillation was managed without using the explicit phase or frequency knowledge. However, phase, frequency, and amplitude modulation emerged to form an efficient synchronized limit cycle. This type of distributed neural integrator can be used as a source for regulating multi-joint coordination to induce synergetic oscillations in natural mechanical systems.

Strong coupling of plasmonic waves in graphene for light confinement

The interplay between light and matter is highly required in many fundamental processes and optical devices. Herein, a hybrid graphene-based coupling system in the far-infrared range is proposed to investigate effective light confinement. In our system, the coupling of localized surface plasmons (LSPs) in graphene nanoribbons and Tamm surface plasmons (TSP) in a graphene sheet produces a hybrid dual-band absorption. This property is numerically verified by full electromagnetic simulations and analytically calculated by the rigorous coupled wave theory (RCWA). The hybrid nature of the two optical modes reflected by coupled oscillator model is discussed carefully, and the influences of incident angle and the geometric parameter on the coupling system are also analyzed. We have found that the coupling strength of the hybrid optical mode can be manipulated flexibly by the incident angle and the geometric parameter. Additionally, the group time delay of the light has also been considered, and calculated values as high as 114 ps. This work offers a new paradigm for tunable light-graphene interaction, and facilitates the design of slow light devices in the far-infrared spectral band.

Learning to predict synchronization of coupled oscillators on randomly generated graphs

Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph structure, this is an important yet analytically intractable question in general. In this work, we take an alternative approach to the synchronization prediction problem by viewing it as a classification problem based on the fact that any given system will eventually synchronize or converge to a non-synchronizing limit cycle. By only using some basic statistics of the underlying graphs such as edge density and diameter, our method can achieve perfect accuracy when there is a significant difference in the topology of the underlying graphs between the synchronizing and the non-synchronizing examples. However, in the problem setting where these graph statistics cannot distinguish the two classes very well (e.g., when the graphs are generated from the same random graph model), we find that pairing a few iterations of the initial dynamics along with the graph statistics as the input to our classification algorithms can lead to significant improvement in accuracy; far exceeding what is known by the classical oscillator theory. More surprisingly, we find that in almost all such settings, dropping out the basic graph statistics and training our algorithms with only initial dynamics achieves nearly the same accuracy. We demonstrate our method on three models of continuous and discrete coupled oscillators—the Kuramoto model, Firefly Cellular Automata, and Greenberg-Hastings model. Finally, we also propose an “ensemble prediction” algorithm that successfully scales our method to large graphs by training on dynamics observed from multiple random subgraphs.

Bistability in dissipatively coupled cavity magnonics

Dissipative coupling of resonators arising from their cooperative dampings to a common reservoir induces intriguingly new physics such as energy level attraction. In this study, we report the nonlinear properties in a dissipatively coupled cavity magnonic system. A magnetic material yttrium iron garnet is placed at the magnetic field node of a Fabry-Perot-like microwave cavity such that the magnons and cavity photons are dissipatively coupled. Under high power excitation, a nonlinear effect is observed in the transmission spectra, showing bistable behaviors. The observed bistabilities are manifested as clockwise, counterclockwise, and butterfly-like hysteresis loops with different frequency detuning. The experimental results are well explained as a Duffing oscillator dissipatively coupled with a harmonic one and the required trigger condition for bistability could be determined quantitatively by the coupled oscillator model. Our results demonstrate that the magnon damping has been suppressed by the dissipative interaction, which thereby reduces the threshold for conventional magnon Kerr bistability. This work sheds light on potential applications in developing low power nonlinearity devices, enhanced anharmonicity sensors and for exploring the non-Hermitian physics of cavity magnonics in the nonlinear regime.

Early detection of synchrony in coupled oscillator model

In this paper, we study the applicability of an early warning index while studying the transitions to complete and generalized synchronizations in the coupled oscillator models using an unconventional system parameter and the coupling strength as the required control parameters. The coupled oscillator models are widely used and well-documented models for studying various aspects of nature. However, the early warning index used in this paper is an explicit function of the mutual information of the coupled oscillators and reaches two different values before the interacting oscillators yield complete and generalized synchronizations. The transitions to synchrony using the unconventional control parameter are associated with a transition to periodic dynamics of the individual oscillators from their initial chaotic dynamics. Besides, when we use the coupling strength as a control parameter, the interacting oscillator exhibits chaotic dynamics during the synchronizations. Our analysis mainly involves different examples of two low-dimensional oscillators. Finally, we extend our study to a network of interacting oscillators. The applicability of the early detection index is verified in all cases.

Strong coupling of exciton and guided mode in perovskite film with high fabrication-tolerant scheme

The strong coupling between guided mode resonance of dielectric grating and excitons in perovskite film is theoretically investigated. It is numerically demonstrated that the strong coupling between guided mode resonance and excitons can enable a significant Rabi splitting. The maximum Rabi splitting up to 362 meV can be achieved through changing the period of the dielectric grating, which is also confirmed theoretically through the coupled-oscillator model. In addition, the effects of the structure dimensions on the strong coupling are also studied in detail, so as to provide theoretical guidance for real fabrication. More importantly, the Rabi splitting could be further enlarged even up to 378 meV by increasing the thickness of the perovskite film. Our findings provide a novel scheme for realizing perovskite-based light-matter interactions and enable related studies on quantum and nonlinear photonic devices.

Hybrid epsilon-near-zero modes of photonic gap antennas

We demonstrate that in photonic gap antennas composed of an epsilon-near-zero (ENZ) layer embedded within a high-index dielectric, hybrid modes emerge from the strong coupling between the ENZ thin film and the photonic modes of the dielectric antenna. These hybrid modes show giant electric field enhancements, large enhancements of the far-field spontaneous emission rate, and a unidirectional radiation response. We analyze both parent and hybrid modes using quasinormal mode theory and find that the hybridization can be well understood using a coupled oscillator model. Under plane-wave illumination, hybrid ENZ antennas can concentrate light and achieve local electric field amplitudes more than two orders of magnitude greater than that of the incident wave. This places them on par with the best plasmonic antennas. In addition, the far-field spontaneous emission rate of a dipole embedded at the antenna hotspot can be increased by more than three orders of magnitude as compared to that in free space, with nearly perfect unidirectional emission.

Application of projection operator method to coarse-grained dynamics with transient potential.

We show that the coarse-grained dynamics model with the time-dependent and fluctuating potential (transient potential) can be derived from the microscopic Hamiltonian dynamics. The concept of the transient potential was first introduced rather phenomenologically, and its relation to the underlying microscopic dynamics has not been clarified yet. This is in contrast to the generalized Langevin equation, the relation of which to the microscopic dynamics is well-established. In this work, we show that the dynamic equationswith the transient potential can be derived for the coupled oscillator model, without any approximations. It is known that the dynamics of the coupled oscillator model can be exactly described by the generalized Langevin-type equations. This fact implies that the dynamic equationswith the transient potential can be utilized as a coarse-grained dynamics model in a similar way to the generalized Langevin equation. Then we show that the dynamic equationsfor the transient potential can also be formally derived for the microscopic Hamiltonian dynamics, without any approximations. We use the projection operator method for the coarse-grained variables and transient potential. The dynamic equationsfor the coarse-grained positions and momenta are similar to those in the Hamiltonian dynamics, but the interaction potential is replaced by the transient potential. The dynamic equationfor the transient potential is the generalized Langevin equationwith the memory effect. Our result justifies the use of the transient potential to describe the coarse-grained dynamics. We propose several approximations to obtain the simplified dynamics model. We show that, under several approximations, the dynamic equationfor the transient potential reduces to the relatively simple Markovian dynamic equationfor the potential parameters. We also show that with several additional approximations, the approximate dynamics model further reduces to the Markovian Langevin-type equationswith the transient potential.

Selective broadband absorption by mode splitting for radiative cooling

A plasmonic-photonic structure based on colloidal lithography was designed for a scalable radiative cooling system and its absorption properties were theoretically investigated. The structure comprises a SiO2 core, which is on top of an Au reflector and partially covered by an indium tin oxide (ITO) shell. This simple and scalable structure possesses a strong selective absorption in the primary atmospheric transparency window (8-13 µm). The strong selective absorption is attributed to a mode splitting of the localized surface plasmon (LSP) of the ITO shell. To understand the mechanisms of the mode splitting, a quantitative analysis was conducted using a coupled-oscillator model and a coupled-dipole method. The analysis revealed that the mode splitting is induced by a strong coupling between the LSP of the ITO shell and a magnetic dipole Mie resonance of the SiO2 core.